Serial dilution calculator

What is a serial dilution?

A chain of dilutions by the same factor: dilute the stock, then dilute that tube the same way, and so on. The American Society for Microbiology’s serial dilution protocol explains that each tube is a dilution of the one before it, so the total dilution of a tube is its own dilution times those of all the previous tubes. Six 1:10 steps give 1:1,000,000.

How do I calculate the dilution factor?

Dilution of a tube = volume transferred ÷ (volume transferred + diluent already in the tube). ASM’s example: 0.5 mL added to 4.5 mL is 0.5/5.0 = 1/10; then 1 mL of that added to 9 mL is another 1/10, a total of 1/100 in the second tube. Each step is the ordinary C₁V₁ = C₂V₂ dilution (OpenStax Chemistry 2e).

How much do I transfer and how much diluent do I use?

For a dilution factor DF and a volume V in each tube: transfer V ÷ DF and add it to V − V ÷ DF of diluent. For 1 mL tubes at 1:10 that is 100 µL into 900 µL; at 1:2 it is 500 µL into 500 µL. Every tube except the last loses the transfer volume when you move on, so it ends with V minus the transfer.

Is 1:10 the same as 1:9?

Not as written. In a dilution, 1:10 (or 1/10) means one part sample in ten parts total — one part sample plus nine parts diluent. Some protocols write the sample-to-diluent ratio 1:9 for the same thing. This calculator uses the dilution factor: final volume ÷ transferred volume.

How many steps do I need to reach a concentration?

Steps = log(C₀ ÷ C_target) ÷ log(DF), rounded up. From 1 mg/mL down to 1 µg/mL (1,000 times) with 1:10 steps takes 3 tubes; with 1:2 steps it takes 10 (2¹⁰ = 1,024). Enter a target to see the count and where each tube lands.

How do I get the original concentration from a plate count?

Divide the colony count by the volume plated (in mL) times the dilution of that tube. If 150 colonies grow from 0.1 mL of the 10⁻⁶ tube, the original sample had 150 ÷ (0.1 × 10⁻⁶) = 1.5 × 10^9 colony-forming units per mL. Plates with roughly 30 to 300 colonies are usually the countable ones.

What each number means

The dilution factor of one tube is the final volume divided by the volume transferred, and the cumulative factor is the product of the factors of all the steps so far: DFⁿ for equal steps. The concentration in tube n is C₀ ÷ DFⁿ. This is a repeated use of C₁V₁ = C₂V₂. To make a 1:10 step in a tube with a final volume V, transfer V ÷ 10 of the previous tube and add nine tenths of V as diluent.

A worked example

Take a stock of 100 mg/mL, a tenfold dilution factor and a final volume of 9 mL in each tube: transfer 0.9 mL into 8.1 mL of diluent for a total of 9 mL. The tubes then hold 10, 1, 0.1, 0.01, 0.001, 0.0001 mg/mL, with cumulative dilutions of 10, 100, 1,000 and so on. To go from 100 mg/mL to 0.001 mg/mL, a hundred-thousandfold dilution, takes 5 tenfold steps or 17 twofold steps. A twofold series from the same stock with 1 mL tubes (0.5 mL transferred into 0.5 mL of diluent) gives 50, 25, 12.5, 6.25 mg/mL.

Common mistakes

Mixing up the ratio notation is the first: 1:10 usually means one part sample in ten parts in total, so one part sample plus nine parts diluent, though some protocols write 1:9 for this. Using the per-tube factor where the cumulative factor is needed, such as in a plate-count calculation, is the second. Third, an error in the first transfer propagates to every later tube, so use a fresh tip for each step and mix thoroughly before transferring. Finally, forgetting the plated volume when converting a colony count to a concentration shifts the answer by a factor of ten when you plate 0.1 mL.

Sources: American Society for Microbiology, serial dilution protocol; OpenStax Chemistry 2e, section 3.3 (dilution, C₁V₁ = C₂V₂). Related: dilution calculator, molarity calculator, ppm calculator and percent to molarity calculator.